On the conjugacy problem for finite-state automorphisms of regular rooted trees

Abstract

We study the conjugacy problem in the automorphism group $Aut(T)$ of a regular rooted tree $T$ and in its subgroup $FAut(T)$ of finite-state automorphisms. We show that under the contracting condition and the finiteness of what we call the orbit-signalizer, two finite-state automorphisms are conjugate in $Aut(T)$ if and only if they are conjugate in $FAut(T)$, and that this problem is decidable. We prove that both these conditions are satisfied by bounded automorphisms and establish that the (simultaneous) conjugacy problem in the group of bounded automata is decidable.

Final version with an appendix by Raphaël M. Jungers

References in corpus (2)

• Branch Rings, Thinned Rings, Tree Enveloping Rings
• Post-critically finite self-similar groups

Cited by in corpus (1)

• The conjugacy problem in automaton groups is not solvable